Skewness

Skewness(x, i, w)

Computes an estimate of the weighted skewness of a distribution, as given by

[math]\displaystyle{ \sum_i w_i \left({x-\bar{x}}\over\sigma\right)^3 / \sum_i w_i }[/math]

A symmetric distribution as zero skew. A distribution with a heavy right tail (like Gamma, LogNormal) is positively skewed. A distribution with a heavy left tail has a negative skew.

If one or more infinite values occur in «x», the Skewness will be +INF, -INF or NaN:

If Min(x) = INF or Max(x) = -INF, then Skewness isNaN.

If Min(x) = -INF and Max(x) = INF then Skewness is NaN.

If Min(x) > -INF and Max(x) = INF, then Skewness is +INF.

If Min(x) = -INF and Max(x) < INF, then Skewness is -INF.

See also

• Statistical Functions and Importance Weighting